How Does the Bent-Walsh Rule Work in Molecules of para-Disubstituted Benzene Derivatives? The Case of para-Nitrophenol and para-Nitrophenolate

DFT (B3LYP/6-311+G**) optimization of nitrobenzene, 4-nitrophenol and 4-nitrophenolate with the constraints for the rotating nitro group, with an interval of 15 degrees, allowed us to show how the Bent-Walsh rule works in a whole range of variation of geometry in the vicinity of both substituted carbon atoms, C1 and C4. For scatter plots of geometry parameters in the vicinity of the C1 carbon atom the general view is in line with the Bent-Walsh rule. The relationship between the mean value of C1C2 and C1C6 bond lengths and the CO bond length has a negative slope, as expected. Two other dependences, this is the above mentioned bond lengths on C6-C1-C2 angle, have also rational slopes but present a relationship between two clusters, for 4-nitrophenol and 4-nitrophenolate, and within these clusters the slopes are opposite, due to the dominant resonance effect over the electronegativity one. In the case of scatter plots of geometry parameters in the vicinity of the C4 carbon atom the general view is again in line with the Bent-Walsh rule, but irregularities are of different shape: they result from strong interactions between oxygen atoms of the nitro group and both CH in ortho positions. These interactions become the strongest for planar conformation of the nitro group and decrease in strength with an increase of the rotation angle. This results in a perturbation in the resonance/electronegativity blend leading to substantial deviations from linear dependences of the CN bond length vs. the mean value of C4C3 and C4C5 bond lengths, and the CN bond length vs. C3-C4-C5 angle.